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Two Wheels Self Balancing Robot

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Southern Taiwan University

Department of Electrical Engineering

Two Wheels Self Balancing Robot

Professor : Chi-Jo Wang

Student’s name : Nguyen Van Binh

Student ID: MA02B203

- Overview of two wheel balancing robot
- Dynamic model
- PID controller
- Implement
- Conclusion

Two wheel balancing robot based on inverted pendulum model.

Inverted pendulum model is a complex nonlinear object. In recent

years there have been many projects about the application of inverted

pendulum principle to make two wheel self balancing robot.

A robot that is capable of balancing upright on its two wheels is

known as a two wheeled balancing robot. The process of balancing is

typically referred to as stability control. The two wheels are situated

below the base and allow the robot chassis to maintain an upright

position by moving in the direction of tilt, either forward or

backward, in an attempt to keep the centre of the mass above the

wheel axles. The wheels also provide the locomotion thus allowing

the robot to transverse across various terrains and environments.

Some applications of two wheels balancing robot

Two wheels balancing robot based on inverted pendulum dynamic

model. So, research about inverted pendulum dynamic model is

necessary in modeling robot . Consider inverted pendulum dynamic

model as following:

With

O-I signals block diagram of model

Inverted pendulum system

Suppose (xp; yp) is coordinate of m heavy at the top of the

pendulum, we have:

Applying Newton's II law of motion in the x, we have:

Change xp in [2-1] into [2-3], we have:

Implement calculating from [2-4]

Applying Newton's II Law for rotation of the pendulum around axis

From [2-1], [2-2], [2-6] we have:

Implement calculating from [2-7]

From [2-5] and [2-8] easy to have:

Suppose F = u

Set state-space, we have:

Balance point at the vertical position:

Linear around at the balance point:

With:

PID is “Proportional, Integral, and derivative”. PID is the three-

term controller.

PID controller based on a feedback control method.

Process is a controlled object. The purpose of control is to

make the output y (PV) followed r set point (set point-SP). To

do this, the controller will get the error between output signal

and input signal and then through the stages of control to make

control signals accordingly, to minimize this error.

A proportional controller (Kp) will have the effect of

reducing the rise time and will reduce ,but never eliminate, the

steady-state error. An integral control (Ki) will have the effect of

eliminating the steady-state error, but it may make the transient

response worse. A derivative control (Kd) will have the effect of

increasing the stability of the system, reducing the overshoot,

and improving the transient response

1. Proportional control

Proportional control generate the changes of output. This

change is proportional to the bias current value. Response of

Proportional control can be adjusted multiplying the difference

signal with Kp.

Pout = Kp.e(t)

with Kp is Gain

e is error = SP-PV

t is current time

With larger Kp value is easy to adjust error. However, the system

lost stability. Kp is too small then the system will react very slowly

with the input error

2. Integral control

The value adjusted at Integral control is proportional with bias

in a period of time. It is total of bias. This signal are then

multiplied by the integral gain Ki and taken to adjust output

With Ioutis the integral of output

Ki is Gain of the integral

e is error = SP-PV

t is current time

Integral control in PID controller increase process to output close

SP value and eliminate setting error of proportional control.

However, Integral control added up all bias in stages before, so It is

cause of overshoot.

3. Derivative control

Derivative control will determine the rate of change of error.

With Doutis the derivative of output

Kd is Gain of the derivative

e is error = SP-PV

t is current time

Integral control in PID controller increase process to output close

SP value and eliminate setting error of proportional control.

However, Integral control added up all bias in stages before, so It is

cause of overshoot.

Accelerometer

PIN9V

Gyro

Source 5V

Microcontroller

ATMEGA32

IR Receiver

L298

PIN 9Vx2

Left wheel motor

Right wheel motor

Figure 4.1 Block Diagram two wheel balancing robot

This project was successful in achieving its aims to

balance a two-wheeled autonomous robot based on the

inverted pendulum model.

The Kalman filter has been successfully implemented.

The gyroscope drift was effectively eliminated allowing

for an accurate estimate of the tilt angle and its derivative

for the robot.

More research is needed to investigate the effects of

linearising the dynamics of the system mode to improve

the stability and robustness of the robot. An attempt to

control the system using nonlinear methods is highly

recommended for future research

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